A student familiar with simultaneously calculating the least common multiple (LCM) and
greatest common factor (GCF), as shared on Ask Dr. Math, re-visits the all-in-one
method. Doctor Peterson expands on his earlier explanation of the technique, then
extends it to apply to three numbers.

Each of three businesses receives different sized cartons of glasses. If
all three receive the same number of glasses and none of them receive
more than a thousand glasses, how many glasses and cartons are in each
shipment?